Theorem equtr 1592

Description: A transitive law for equality. (Contributed by NM, 23-Aug-1993.)

Assertion

Ref	Expression
equtr	|- (x = y -> (y = z -> x = z))

Proof of Theorem equtr

Step	Hyp	Ref	Expression
1		ax-8 1392	. 2 |- (y = x -> (y = z -> x = z))
2	1	equcoms 1591	1 |- (x = y -> (y = z -> x = z))

Syntax hints:   -> wi 4

This theorem was proved from axioms:  ax-1 5  ax-2 6  ax-mp 7  ax-ia1 99  ax-gen 1335  ax-ie2 1380  ax-8 1392  ax-17 1416  ax-i9 1420

This theorem depends on definitions:  df-bi 110

This theorem is referenced by:  equtrr  1593  equequ1  1595  equveli  1639  equvin  1740